past papers Flashcards

1
Q

what is a hypothesis

A

a hypothesis is a statement about a model parameter

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2
Q

Define observed information for 1 single param

A
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3
Q

What is a sufficient statistic

A
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4
Q

Def profile likelihood

A
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5
Q

Def 1 sided hypothesis test

A
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6
Q

Def marginal likelihood in Bayes theorem

A
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7
Q

Find minimal sufficient stat

A

Identity pdf
Identify joint pdf
Apply factorisation theorem (find h(x) that doesn’t depend on θ)

Then for minimal

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8
Q

When finding fisher information remember to

A

Switch to single variable case

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9
Q

Method of moments

A

Where moments are acquired/given earlier

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10
Q

Prove consistency

A

Use LLN (+CMT if necessary)

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11
Q

LLN

A

Sn

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12
Q

Difference between strong and weak LLN

A

If mean is finite => weak (converges in P to μ)
If mean AND var is finite => strong (a.s coverages to μ)

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13
Q

Bayes theorem

A
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14
Q

When determining conjugate prior remember to

A

Only include the kernel of the distribution

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15
Q

When asked about n -> inf

For bayesian point estimator

A

Divide through by n to see dominant terms

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16
Q

Def pivotal quantity

A

A function of the observation and the parameters for which the distribution is entirely specified

17
Q

Showing that a quantity is pivotal

A

Show that it’s distribution doesn’t depend on the parameter of interest

18
Q

Power and size of test

A